Question: If $x \bigtriangledown y = x(y-3)$ and $x \boxdot y = x^{2}+3y^{2}$, find $2 \bigtriangledown (-3 \boxdot 1)$.
Answer: First, find $-3 \boxdot 1$ $ -3 \boxdot 1 = (-3)^{2}+3(1^{2})$ $ \hphantom{-3 \boxdot 1} = 12$ Now, find $2 \bigtriangledown 12$ $ 2 \bigtriangledown 12 = 2(12-3)$ $ \hphantom{2 \bigtriangledown 12} = 18$.